Abstract

Abstract Qualitative modeling concerns the representations and reasoning that people use to understand continuous aspects of the world. Qualitative models formalize everyday notions of causality and provide accounts of how to ground symbolic, relational representations in perceptual processes. This article surveys the basic ideas of qualitative modeling and their applications from a cognitive science perspective. It describes the basic principles of qualitative modeling, and a variety of qualitative representations that have been developed for quantities and for relationships between them, providing a kind of qualitative mathematics. Three ontological frameworks for organizing modeling knowledge (processes, components, and field) are summarized, along with research on automatically assembling models for particular tasks from such knowledge. Qualitative simulation and how it carves up time into meaningful units is discussed. We discuss several accounts of causal reasoning about dynamical systems, based on different choices of qualitative mathematics and ontology. Qualitative spatial reasoning is explored, both in terms of relational systems and visual reasoning. Applications of qualitative models of particular interest to cognitive scientists are described, including how they have been used to capture the expertise of scientists and engineers and how they have been used in education. Open questions and frontiers are also discussed, focusing on relationships between ideas developed in the qualitative modeling community and other areas of cognitive science. WIREs Cogni Sci 2011 2 374–391 DOI: 10.1002/wcs.115 This article is categorized under: Computer Science > Artificial Intelligence Psychology > Reasoning and Decision Making

Images

Qualitative states impose a discrete structure on time. Intervals over which qualitative values are the same are carved up into distinct states. Transitions to a threshold require an interval of time, while transitions from a threshold occur instantaneously. Here, the motion of the ball is broken up into three distinct qualitative states, based on the kind of motion that is occurring, which is determined by the Y velocity.

Example of a food web created from protocol data. This causal model reflects a particular participant's response when asked what would happen if the number of bears in the forest they live near were to decrease. Influences nodes represent qualitative proportionalities, increases/decreases nodes indicate I+, I− relationships.

Example of a place vocabulary for reasoning about motion through space. Part (a) shows a 2D scene, involving a ball and several surfaces. Visual analysis of the scene, guided by the constraint of reasoning about motion, imposes a decomposition of the scene. The dashed lines in part (b) show boundaries between free space regions. Part (c) shows the places constructed. Triangles indicate boundaries between free space regions, and rectangles indicate surfaces. The orientation of the surface icons indicates the qualitative orientation of the original surfaces, and the arcs are labeled with directions (not shown). Free space regions whose top is free and whose other sides are bounded by surfaces is identified as a well.

References

Most of the literature in qualitative modeling is freely available on‐line. For example, the papers from the proceedings of the International Qualitative Reasoning Workshop, which started in 1987, are available at several mirror sites. A number of systems that use qualitative modeling, including Kuipers` QSIM, Bredeweg`s GARP3, Yip and Zhao`s Spatial Aggregation Language, and Northwestern`s VModel, CyclePad, and CogSketch are available as free downloads.